Multipartite bound entanglement and multi-setting Bell inequalities

Details Multipartite bound entanglement and multi-setting Bell inequalities Multipartite bound entanglement and multi-setting Bell inequalities

2009-04-30

arxiv.org/abs/0904.4818v1

Phys. Rev. A 80, 032330 (2009).

Physics

Quantum Physics

4 pages, 2 figures

Scientific paper

D\"{u}r [Phys. Rev. Lett. {\bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the Bell inequality if and only if $N\ge 6$ [Phys. Rev. A {\bf 79}, 032309 (2009)]. On the other hand, it has been also shown that the states which D\"{u}r considered violate Bell inequalities different from the inequality for $N\ge 6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with $M$ settings of the measuring apparatus for sufficiently large $M$, we prove that there exists an $N$-qubit bound entangled state violating the $M$-setting Bell inequality if and only if $N\ge 4$.

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